演示文稿周期性边界条件

优质文档精选周期性边界条件当前1页，总共26页。AnalysisofthePotentialEnergyExternalpotentialPairpotentialabout90%ThreebodycontributionInFCCcrystal,upto10%Effectivepairpotential当前2页，总共26页。1.7.1EffectivepairpotentialforsphericalmoleculesHard-spherepotentialForthepurposesofinvestigatinggeneralpropertiesofliquidsandforcomparisonwiththeory,highlyidealizedpairpotentialsmaybeofvalue.Inthissection,Iwillintroducehard-sphere,square-well,YukawaandLennard-Jonespotentials,etc.isthediameterofhardspheres当前3页，总共26页。Square-WellpotentialSWpotentialisthesimplestoneincludingtheattractiveforcesandcanbeappliedtoinertgasesandsomenon-polarsubstances,etc.当前4页，总共26页。YukawapotentialWhen,itcanbeusedtomodelArreasonablywell.Yukwapotentialcanalsobeusedtomodelplasma,colloidalparticles,andsomeelectricalinteractions.当前5页，总共26页。Lennard-JonespotentialForargon:当前6页，总共26页。CodesforcalculatingthetotalpotentialV=0.0DO100I=1,N-1RXI=RX(I)RYI=RY(I)RZI=RZ(I) DO100J=I+1,N RXIJ=RXI-RX(J) RYIJ=RYI-RY(J) RZIJ=RZI-RZ(J) RIJSQ=RXIJ**2+RYIJ**2+RZIJ**2 SR2=SIGSQ/RIJSQ SR6=SR2*SR2*SR2 SR12=SR6**2 V=V+SR12-SR6100CONTINUEV=V*4.0*EPSLONThecoordinatevectorsofLJatomsarestoredinthreearraysRX(I),RY(I),RZ(I)Calculate当前7页，总共26页。PotentialsforionsAsimpleapproachtoconstructpotentialsforionsistosupplementoneoftheabovepairpotentialswiththeCoulombcharge-chargeinteraction:WhereXmaybeHS,SW,LJ.Thepopularoneis:当前8页，总共26页。1.7.2potentialformacromoleculesTheenergy,V,isafunctionoftheatomicpositions,R,ofalltheatomsinthesystem,theseareusuallyexpressedintermofCartesiancoordinates.Thevalueoftheenergyiscalculatedasasumofinternal,orbondedterms,whichdescribethebonds,anglesandbondrotationsinamolecule,andasumofexternalornonbondedterms.Thesetermsaccountforinteractionsbetweennonbondedatomsoratomsseparatedby3ormorecovalentbonds.当前9页，总共26页。BondedpotentialBondangle-bendBond-strentchTorsion(rotate-along-bond)当前10页，总共26页。Angle-bendpotentialThedeviationofanglesfromtheirreferencevaluesisfrequentlydescribedusingaHooke’slaworharmonicpotential:当前11页，总共26页。Bond-stretchpotential当前12页，总共26页。TorsionpotentialTorsionalpotentialsarealmostalwaysexpressedasacosineseriesexpansion.‘barrier’heightDetermineswherethetorsionanglepassesthroughitsminimumvalue.Thenumberofminimumpointsinthefunctionasthebondisrotatedthrough2.当前13页，总共26页。1.8ReducedUnitsWhyusereducedunit?Avoidsthepossibleembarrassmentofconductingessentiallyduplicatesimulations.Andtherearealsotechnicaladvantagesintheuseofreducedunitsduetothesimulationboxisinthemagnitudeofmolecularscale.Density

Temperature

Energy

Pressure

Force

Torque

SurfacetensionTime当前14页，总共26页。Reducedunit----continueDiffusioncoefficient

ViscosityThermalconductivitySIUnits:W/(mK)Pasm2/sTestofunit(Forexample,viscosity):当前15页，总共26页。Reducedunit----continueItshouldbepointedthatallthereducedunitsintheprevioustwoslidesarebasedonLennard-Jonesinteractionpotential.Forhardspherefluid,thereducedunitsareobtainedusingkBTtoreplace.Thereducedunitsforotherpropertiessuchaschemicalpotentialandheatcapacitycanbededucedfromtheunitsgiveninthissection.Especially,forelectrolytesolution,wecanuseSurfacechargedensity:当前16页，总共26页。1.9SimulationBoxandItsBoundaryConditionsComputersimulationsareusuallyperformedonasmallnumberofmolecules,10<N<10,000.ThetimetakenforadoubleloopusedtoevaluatetheforcesandpotentialenergyisproportionaltoN2.Whetherornotthecubeissurroundedbyacontainingwall,moleculesonthesurfacewillexperiencequitedifferentforcesfrommoleculesinthebulk.Itisessentialtoproposepropermethodstoovercometheproblemofsurfaceeffects.当前17页，总共26页。1.9.1SimulationboxxyzCubeHexagonalprismxyzExample:DNAsimulation当前18页，总共26页。1.9.1Simulationbox---continueTruncatedoctahedronRhombicdodecahedron当前19页，总共26页。1.9.2PeriodicboundaryconditionBAHDGFEC当前20页，总共26页。BAHDGFECInacubicbox,thecutoffdistanceissetequaltoL/2.

Minimumimageconvention当前21页，总共26页。AEAsideviewofthebox(b)AtopviewoftheboxBDCAEHFGSimulationofmoleculesinslit-likepore当前22页，总共26页。1.9.3ComputercodeforperiodicboundariesHowdowehandleperiodicboundariesandtheminimumimageconventioninasimulationprogram?Letusassume,initially,theNmoleculesinthesimulationliewithacubicboxofsideBOXL,withtheoriginatitscenter,i.e.,allcoordinatelieintherange(-BOXL/2,BOXL/2).Afterthemoleculeshavebeenmoved,wemusttestthepositionimmediatelyusingaFORTRANIF

statement.IF(RX(I).GT.BOXL2)RX(I)=RX(I)-BOXLIF(RX(I).LT.-BOXL2)RX(I)=RX(I)+BOXL当前23页，总共26页。AnalternativecodeforperiodicboundariesAnalternativetotheIFstatementistouseFORTRANarithmetic

functions:RX(I)=RX(I)-BOXL*ANINT(RX(I)/BOXL)ThefunctionANINT(X)returnsthenearestintegertoX,convertingtheresultsbacktotypeREAL.Forexample,ANINT(-0.49)=0;ANINT(-0.55)=-1

ThefunctionANINT(X)isdifferentfromAINT(X).AINT(X)returnstheintegralpartofX.TheuseofIFstatementinsidetheinnerloop,particularlyonpipelinemachines,istobeavoided.当前24页，总共26页。1.9.4ComputercodeforminimumimageconventionImmediatelyaftercalculatinga